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Symmetric Arithmetic Circuits.

Published version
Peer-reviewed

Type

Conference Object

Change log

Authors

Wilsenach, Gregory 

Abstract

We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the restriction amounts to requiring that the shape of the circuit is invariant under row and column permutations of the matrix. We establish unconditional, nearly exponential, lower bounds on the size of any symmetric circuit for computing the permanent over any field of characteristic other than 2. In contrast, we show that there are polynomial-size symmetric circuits for computing the determinant over fields of characteristic zero.

Description

Keywords

Journal Title

ICALP

Conference Name

47th International Colloquium on Automata, Languages, and Programming

Journal ISSN

1868-8969

Volume Title

168

Publisher

Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Sponsorship
Engineering and Physical Sciences Research Council (EP/S03238X/1)